At the beginning of the film a calendar is seen showing the time as June, 1934. Yet months later, when Lillian is in Europe and reads about the riots which lead to an injury of her friend Julia, the American newspaper she reads has a date of Feb.,1934.
The same locomotive is pulling the train from Berlin to Moscow even though it is a different train. In addition, a single steam locomotive would never have been used from Paris to Berlin, let alone Paris to Moscow.
During a sailing shot, as the boat containing Julia and Lilian tracks away from the camera, the gunnel of the boat containing the camera crew is clearly visible for an instant in the lower left of the frame.
When Lillian (Jane Fonda) is Entering The Tuileries Garden with Johann (Maximilian Schell) in The Long Shot;The Windshields of Modern Day Cars Can Be Seen "Zooming" Past (The Louvre) Faster Than Cars of the Time Period Would.
The goof item below may give away important plot points.
The plot of the entire film revolves around the restrictions in pre-WWII Nazi Germany on the import of foreign (such as American) currency. There was no such restriction. Stable foreign currency was welcomed in an era when extreme inflation was a recent memory.